Question

The length, breadth and height of a cuboid are in the ratio 5:4:2. If the total surface area is 1216 cm², Find the dimensions of the solid.

Answer 1

Let:
Length of the cuboid, l = 5x cm
Breadth of the cuboid, b = 4x cm
Height of the cuboid, h = 2x cm

Total surface area of the cuboid = 2(lb + bh + hl)

$$\begin{gathered} \Rightarrow 1216=2\left\{\right(5x)\times (4x)+(4x)\times (2x)+(2x)\times (5x\left)\right) \\ \Rightarrow 1216=2\{20x^2+8x^2+10x^2\} \\ \Rightarrow 1216=2\{38x^2\} \\ \Rightarrow 1216=76x^2 \\ \Rightarrow x^2=16 \\ \Rightarrow x=4 \end{gathered}$$
Thus, we have:
Length of the cuboid, l = 5$\times$4 = 20 cm
Breadth of the cuboid, b = 4$\times$4 = 16 cm
Height of the cuboid, h = 2$\times$4 = 8 cm